1. **State the problem:** Calculate the volume of a right-angled triangular prism with legs 23 m and 38 m, and length (depth) 11 m. 2. **Formula:** The volume $V$ of a prism is given by the area of the base $A$ times the length $L$: $$V = A \times L$$ 3. **Calculate the area of the triangular base:** For a right-angled triangle, the area is: $$A = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$$ Here, $\text{leg}_1 = 23$ m and $\text{leg}_2 = 38$ m. 4. **Calculate the area:** $$A = \frac{1}{2} \times 23 \times 38 = \frac{1}{2} \times 874 = 437 \text{ m}^2$$ 5. **Calculate the volume:** $$V = A \times L = 437 \times 11 = 4807 \text{ m}^3$$ 6. **Round to 1 decimal place:** $$V = 4807.0 \text{ m}^3$$ **Final answer:** The volume of the prism is $4807.0$ cubic meters.